Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets

Details Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets

2002-05-06

arxiv.org/abs/cond-mat/0205105v1

Physics

Condensed Matter

Superconductivity

12 pages, 11 figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.66.104503

We report a study of overdamped Josephson junction arrays with the geometry of periodically repeated Sierpinski gaskets. These model superconductors share essential geometrical features with truly random (percolative) systems. When exposed to a perpendicular magnetic field B, their euclidian or fractal behavior depends on the relation between the intervortex distance (imposed by B) and the size of a constituent gasket, and was explored with high-resolution measurements of the sample magnetoinductance L(B). In terms of the frustration parameter f expressing (in units of the superconducting flux quantum) the magnetic flux threading an elementary triangular cell of a gasket, the crossover between the two regimes occurs at f_{cN}=1/(2*4^{N}), where N is the gasket order. In the fractal regime (f>f_{cN}) a sequence of equally spaced structures corresponding to the set of states with unit cells not larger than a single gasket is observed at multiples of f_{cN}, as predicted by theory. The fine structure of L(f) radically changes in the euclidian regime (f

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